{
 "metadata": {
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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  "kernelspec": {
   "name": "python3",
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  }
 },
 "nbformat": 4,
 "nbformat_minor": 2,
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 数据归一化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 最值归一化 Normaliztion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.random.randint(0, 100, size=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([98, 59, 50, 23, 17, 14, 14, 74, 44,  2, 10, 16, 50, 77, 34, 24,  4,\n       20, 16, 37,  2, 77, 70, 42, 84, 94, 11, 93, 70, 79, 89, 45, 31, 58,\n       75, 16, 65, 46, 87, 16, 13, 78, 91, 38, 96, 51, 18, 54, 86, 55, 50,\n       82, 50, 31,  7, 24, 59, 53, 91, 72, 67, 71, 35, 24, 23, 23, 97, 34,\n       91, 80, 54, 37,  1, 37, 52, 38, 54, 53, 32, 93, 51, 28, 88, 70, 98,\n       84, 77, 81, 18,  6, 36, 31, 73, 90, 58, 47, 99, 76, 24, 76])"
     },
     "metadata": {},
     "execution_count": 3
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([0.98979592, 0.59183673, 0.5       , 0.2244898 , 0.16326531,\n       0.13265306, 0.13265306, 0.74489796, 0.43877551, 0.01020408,\n       0.09183673, 0.15306122, 0.5       , 0.7755102 , 0.33673469,\n       0.23469388, 0.03061224, 0.19387755, 0.15306122, 0.36734694,\n       0.01020408, 0.7755102 , 0.70408163, 0.41836735, 0.84693878,\n       0.94897959, 0.10204082, 0.93877551, 0.70408163, 0.79591837,\n       0.89795918, 0.44897959, 0.30612245, 0.58163265, 0.75510204,\n       0.15306122, 0.65306122, 0.45918367, 0.87755102, 0.15306122,\n       0.12244898, 0.78571429, 0.91836735, 0.37755102, 0.96938776,\n       0.51020408, 0.17346939, 0.54081633, 0.86734694, 0.55102041,\n       0.5       , 0.82653061, 0.5       , 0.30612245, 0.06122449,\n       0.23469388, 0.59183673, 0.53061224, 0.91836735, 0.7244898 ,\n       0.67346939, 0.71428571, 0.34693878, 0.23469388, 0.2244898 ,\n       0.2244898 , 0.97959184, 0.33673469, 0.91836735, 0.80612245,\n       0.54081633, 0.36734694, 0.        , 0.36734694, 0.52040816,\n       0.37755102, 0.54081633, 0.53061224, 0.31632653, 0.93877551,\n       0.51020408, 0.2755102 , 0.8877551 , 0.70408163, 0.98979592,\n       0.84693878, 0.7755102 , 0.81632653, 0.17346939, 0.05102041,\n       0.35714286, 0.30612245, 0.73469388, 0.90816327, 0.58163265,\n       0.46938776, 1.        , 0.76530612, 0.23469388, 0.76530612])"
     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "source": [
    "(x - np.min(x)) / (np.max(x) - np.min(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.random.randint(0 ,100, (50, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[31, 12],\n       [96, 48],\n       [70, 68],\n       [22, 52],\n       [38, 49],\n       [85, 82],\n       [76, 94],\n       [51, 94],\n       [88, 85],\n       [96, 21]])"
     },
     "metadata": {},
     "execution_count": 9
    }
   ],
   "source": [
    "X[:10, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.array(X, dtype=float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[31., 12.],\n       [96., 48.],\n       [70., 68.],\n       [22., 52.],\n       [38., 49.],\n       [85., 82.],\n       [76., 94.],\n       [51., 94.],\n       [88., 85.],\n       [96., 21.]])"
     },
     "metadata": {},
     "execution_count": 11
    }
   ],
   "source": [
    "X[:10, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "X[:,0] = (X[:,0] - np.min(X[:,0])) / (np.max(X[:,0]) - np.min(X[:,0]))\n",
    "X[:,1] = (X[:,1] - np.min(X[:,1])) / (np.max(X[:,1]) - np.min(X[:,1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([[0.30612245, 0.12121212],\n       [0.96938776, 0.48484848],\n       [0.70408163, 0.68686869],\n       [0.21428571, 0.52525253],\n       [0.37755102, 0.49494949],\n       [0.85714286, 0.82828283],\n       [0.76530612, 0.94949495],\n       [0.51020408, 0.94949495],\n       [0.8877551 , 0.85858586],\n       [0.96938776, 0.21212121]])"
     },
     "metadata": {},
     "execution_count": 14
    }
   ],
   "source": [
    "X[:10, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.scatter(X[:,0], X[:,1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "0.5081632653061223"
     },
     "metadata": {},
     "execution_count": 16
    }
   ],
   "source": [
    "np.mean(X[:,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "0.3366914010512558"
     },
     "metadata": {},
     "execution_count": 18
    }
   ],
   "source": [
    "np.std(X[:,0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 均值方差归一化 Standardiztion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "X2= np.random.randint(0, 100,(50,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "X2 = np.array(X2, dtype=float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "X2[:,0] = (X2[:,0] - np.mean(X2[:,0])) / np.std(X2[:,0])\n",
    "X2[:,1] = (X2[:,1] - np.mean(X2[:,1])) / np.std(X2[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.scatter(X2[:,0], X2[:,1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "1.3322676295501878e-17"
     },
     "metadata": {},
     "execution_count": 23
    }
   ],
   "source": [
    "np.mean(X2[:,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "1.0"
     },
     "metadata": {},
     "execution_count": 24
    }
   ],
   "source": [
    "np.std(X2[:,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ]
}